The integrity of safety-critical structural composites can be enhanced by the use of innovative ultrasonic nondestructive evaluation (NDE) techniques. Among the various existing techniques, guided wave methods provide a good compromise in terms of sensitivity to a variety of damage types or defects and extent of the area that can be monitored, given the ability of this waves to travel relatively long distances within the structure under investigation. In comparison with Lamb waves propagating in isotropic structures, wave propagation in composite structures presents additional complexity for effective damage identification. The material inhomogeneity, the anisotropy and the multi-layered construction lead to the significant dependence of wave modes on laminate layup configurations, direction of propagation, frequency, and interface conditions. In this paper a specific structure will be analyzed with different levels of complexities as far as the wave propagation characteristics are concerned. The investigated structure is a composite stiffened plate. The work is carried out using theoretical analysis, numerical models and experimental verifications. Numerical (Finite Element) models are used for more practical cases, for which the geometric and material complexities of actual structures present practical difficulties in direct analysis of wave propagation data using theoretical constructs only.